Partition function zeros at first-order phase transitions: Pirogov-Sinai theory

Details Partition function zeros at first-order phase transitions: Pirogov-Sinai theory Partition function zeros at first-order phase transitions: Pirogov-Sinai theory

2003-12-14

arxiv.org/abs/math-ph/0312041v2

J. Statist. Phys. 116 (2004), no. 1-4, 97-155

Physics

Mathematical Physics

46 pages, 2 figs; continuation of math-ph/0304007 and math-ph/0004003, to appear in J. Statist. Phys. (special issue dedicated

Scientific paper

10.1023/B:JOSS.0000037243.48527.

This paper is a continuation of our previous analysis [BBCKK] of partition functions zeros in models with first-order phase transitions and periodic boundary conditions. Here it is shown that the assumptions under which the results of [BBCKK] were established are satisfied by a large class of lattice models. These models are characterized by two basic properties: The existence of only a finite number of ground states and the availability of an appropriate contour representation. This setting includes, for instance, the Ising, Potts and Blume-Capel models at low temperatures. The combined results of [BBCKK] and the present paper provide complete control of the zeros of the partition function with periodic boundary conditions for all models in the above class.

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